NAG Library Function Document

nag_bessel_k_alpha (s18egc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{x}$ – doubleInput

On entry: the argument $x$ of the function.

Constraint: $\mathbf{x}>0.0$.

2:    $\mathbf{ia}$ – IntegerInput

3:    $\mathbf{ja}$ – IntegerInput

On entry: the numerator $i$ and denominator $j$, respectively, of the order $\alpha =i/j$ of the first member in the required sequence of function values. Only the following combinations of pairs of values of $i$ and $j$ are allowed:

• $i=0$ and $j=1$ corresponds to $\alpha =0$;
• $i=1$ and $j=2$ corresponds to $\alpha =\frac{1}{2}$;
• $i=1$ and $j=3$ corresponds to $\alpha =\frac{1}{3}$;
• $i=1$ and $j=4$ corresponds to $\alpha =\frac{1}{4}$;
• $i=2$ and $j=3$ corresponds to $\alpha =\frac{2}{3}$;
• $i=3$ and $j=4$ corresponds to $\alpha =\frac{3}{4}$.

Constraint: ia and ja must constitute a valid pair $\left(\mathbf{ia},\mathbf{ja}\right)=\left(0,1\right)$, $\left(1,2\right)$, $\left(1,3\right)$, $\left(1,4\right)$, $\left(2,3\right)$ or $\left(3,4\right)$.

4:    $\mathbf{nl}$ – IntegerInput

On entry: the value of $N$. Note that the order of the last member in the required sequence of function values is given by $\alpha +N$.

Constraint: $0\le \mathbf{nl}\le 100$.

5:    $\mathbf{b}\left[\mathbf{nl}+1\right]$ – doubleOutput

On exit: with $\mathbf{fail}\mathbf{.}\mathbf{code}=\mathrm{NE\_NOERROR}$ or $\mathbf{fail}\mathbf{.}\mathbf{code}=\mathbf{NW\_SOME\_PRECISION\_LOSS}$, the required sequence of function values: b$\left(n\right)$ contains $K_{\alpha +n}\left(x\right)$ for $n=0,1,\dots ,N$.

6:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_INT

On entry, $\mathbf{nl}=〈\mathit{\text{value}}〉$.
Constraint: $0\le \mathbf{nl}\le 100$.

NE_INT_2

On entry, $\mathbf{ia}=〈\mathit{\text{value}}〉$, $\mathbf{ja}=〈\mathit{\text{value}}〉$.
Constraint: ia and ja must constitute a valid pair (ia,ja).

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NE_OVERFLOW_LIKELY

The evaluation has been abandoned due to the likelihood of overflow.

NE_REAL

On entry, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}>0.0$.

NE_TERMINATION_FAILURE

The evaluation has been abandoned due to failure to satisfy the termination condition.

NE_TOTAL_PRECISION_LOSS

The evaluation has been abandoned due to total loss of precision.

NW_SOME_PRECISION_LOSS

The evaluation has been completed but some precision has been lost.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (s18egce.c)

10.2

Program Data

Program Data (s18egce.d)

10.3

Program Results

Program Results (s18egce.r)